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An Application of Total-Colored Graphs to Describe Mutations in Non-Mendelian Genetics

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Department of Applied Mathematics I, University of Seville, 41012 Sevilla, Spain
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Department of Geometry and Topology, University of Seville, 41012 Sevilla, Spain
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Author to whom correspondence should be addressed.
Mathematics 2019, 7(11), 1068; https://doi.org/10.3390/math7111068
Received: 16 September 2019 / Revised: 1 November 2019 / Accepted: 3 November 2019 / Published: 6 November 2019
(This article belongs to the Special Issue Graph-Theoretic Problems and Their New Applications)
Any gene mutation during the mitotic cell cycle of a eukaryotic cell can be algebraically represented by an isotopism of the evolution algebra describing the genetic pattern of the inheritance process. We identify any such pattern with a total-colored graph so that any isotopism of the former is uniquely related to an isomorphism of the latter. This enables us to develop some results on graph theory in the context of the molecular processes that occur during the S-phase of a mitotic cell cycle. In particular, each monochromatic subset of edges is identified with a mutation or regulatory mechanism that relates any two statuses of the genotypes of a pair of chromatids.
Keywords: evolution theory; evolution algebra; mitotic cell cycle; total-colored graph evolution theory; evolution algebra; mitotic cell cycle; total-colored graph
MDPI and ACS Style

Falcón, R.M.; Falcón, Ó.J.; Núñez, J. An Application of Total-Colored Graphs to Describe Mutations in Non-Mendelian Genetics. Mathematics 2019, 7, 1068.

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